Question

What is the radian measure of the central angle of an arc that has an arc length of 3 units and a radius of 4 units?

Find the arc length intercepted by a central angle of pi/2 radians in a circle whose radius is 24 inches.

Find the measure of a central angle that intercepts an arc of 27 inches in a circle whose radius is 10 inches.

Answer 1

Explanation:

What is the measure of the central angle?

Answer : 140°

What ratio represents the measure of the central angle compared to the measure of the entire circle?

Answer7/18

If s = , what is the length of minor arc AB?

Answer : 14π

Answer 2

The radius of circle(r), the arc length(s) and the angle subtended by the arc at the center of the circle(Ф) are related by the following equation:

s = rФ

For the first question, we have the arc length (3 units) and the radius of circle (4 units) and we need to find the radian measure of central angle of the arc. Substituting the values in the above formula we get:

3=4Ф
⇒
Ф=3/4 = 0.75 radians


For the second question, we have the central angle (π/2 radians) and the radius of circle(24 inches). We need to find the length of the arc. Substituting the values in above equation, we get:

s = 24 x (π/2) = 12π inches

The third question is similar to the first one. The arc length is given (27 inches) and radius of circle is given to be (10 inches). We are to find the radian measure of central angle. Substituting the values in above equation, we get:

27=10Ф
⇒
Ф=2.7 radians